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Minimizing the Expected Market Time to Reach a Certain Wealth Level

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Abstract

In a financial market model, we consider variations of the problem of minimizing the expected time to upcross a certain wealth level. For exponential Levy markets, we show the asymptotic optimality of the growth-optimal portfolio for the above problem and obtain tight bounds for the value function for any wealth level. In an Ito market, we employ the concept of market time, which is a clock that runs according to the underlying market growth. We show the optimality of the growth-optimal portfolio for minimizing the expected market time to reach any wealth level. This reveals a general definition of market time which can be useful from an investor’s point of view. We utilize this last definition to extend the previous results in a general semimartingale setting.

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File URL: http://www.business.uts.edu.au/qfrc/research/research_papers/rp-230.pdf
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Bibliographic Info

Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 230.

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Length: 15
Date of creation: 01 Aug 2008
Date of revision:
Handle: RePEc:uts:rpaper:230

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Keywords: Numeraire portfolio; growth-optimal portfolio; market time; upcrossing; overshoot; exponential Levy markets; Ito markets; semimartingale markets;

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  1. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151.
  2. Kardaras, Constantinos & Platen, Eckhard, 2011. "On the semimartingale property of discounted asset-price processes," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2678-2691, November.
  3. Constantinos Kardaras & Eckhard Platen, 2008. "On Financial Markets where only Buy-And-Hold Trading is Possible," Research Paper Series 213, Quantitative Finance Research Centre, University of Technology, Sydney.
  4. Dirk Becherer, 2001. "The numeraire portfolio for unbounded semimartingales," Finance and Stochastics, Springer, vol. 5(3), pages 327-341.
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Cited by:
  1. Zeng, Xudong, 2010. "Optimal reinsurance with a rescuing procedure," Insurance: Mathematics and Economics, Elsevier, vol. 46(2), pages 397-405, April.
  2. Eckhard Platen, 2009. "A Benchmark Approach to Investing and Pricing," Research Paper Series 253, Quantitative Finance Research Centre, University of Technology, Sydney.

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